# Thin Airfoil with a Flap

Movable surfaces on airfoils or wings are called flaps (i. e., high-lift devices) or ailerons. Ailerons provide roll or lateral control for the aircraft. Similar movable surfaces on the horizontal stabilizer and vertical fin supply pitch and yaw control. These are usually called the elevator and rudder, respectively.

We consider a two-dimensional airfoil at the angle of attack. Then:

l ‘ = 2 pvjcoc.

Now, think of this airfoil as being part of a wing. If the aircraft is slowing down in the landing process, then the velocity is decreasing. However, the lift must nearly equal the aircraft weight because the vertical acceleration is (hopefully) very small. This means that as the velocity decreases, the lift coefficient must increase (for constant wing area), which in turn means that the angle of attack must increase. This larger angle of attack may be dangerously close to the stalling angle, or at least result in an undesirable nose-up landing attitude. The alternative is a high-lift device—a flap—to generate a higher lift coefficient at the same angle of attack.

The effects of a 20 percent-chord simple split flap deflected 60° are shown in Fig. 5.26 for the NACA 0009 airfoil. Data points for this configuration are the inverted triangles. Tests were performed at a Re of R = 6.0 • 106. One set of tests was arried out with “standard roughness,” which indicates that the surface was not glass smooth as in most of the experiments. When the flap is deployed, the flow reacts as if the positive camber of the airfoil has increased. Because the flap is near the trailing edge, the effect of this increased camber is to make the angle of zero lift significantly larger in magnitude—in this case, aL0 = -12°—and thus to increase the lift coefficient at a particular geometric angle of attack. The value of the maximum lift coefficient (Clmax) also is increased; notice the significant increase in Clmax (i. e., from about 1.3 to 2.1 for this airfoil). The results show that changing the effective camber of the airfoil has a minor effect on lift-curve slope; the primary effects are the change in aL0 and the increased maximum lift coefficient. Figure 5.26 also indicates that the flap deflection causes the angle of stall to be reduced, but this reduction is not large enough to detract from the advantageous shift in the lift curve due to the larger negative-zero-lift angle.

In the case of differential deflection of the ailerons at the wing tips, the camber at one tip is increased while the camber at the other tip is decreased. Because the ailerons are placed in a high-sensitivity location near the trailing edge, and because they are situated near the tips of the wings with long lever arms about the fuselage axis, a small deflection of the ailerons is sufficient to cause a differential lift at the two wing tips that is large enough to roll the airplane.

There are many types of flaps (see Refs. 2-10). So-called slats located at the air­foil leading edge modify the airfoil camber and also force air tangentially along the upper surface of the airfoil, which delays airfoil stall. Devices located at the trailing edge are more effective than leading-edge devices (by about a factor of 3) because of the greater distance from the airfoil quarter-chord point. Flaps at the trailing edge may be single – or multi-element (e. g., a jet transport configured for landing). The geometry of the high-lift multi-element device provides an increase in camber and circulation, and the slots between the elements serve to duct high-pressure air from the lower surface to the upper surface of the flap, thereby delaying boundary-layer separation on the highly curved upper surface. These effects are discussed in detail in Chapter 8.